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King School has an enrollment of 900 students. The school day consists : Problem Solving (PS)
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# King School has an enrollment of 900 students. The school day consists

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Re: King School has an enrollment of 900 students. The school day consists [#permalink]
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total classes 900/30 = 30
and each class has 6 periods so total periods in school ; 30*6
1 teacher takes at most 5 classes so total teachers in school ; 30*6/5 = 36
IMO C

gmatt1476 wrote:
King School has an enrollment of 900 students. The school day consists of 6 class periods during which each class is taught by one teacher. There are 30 students per class. Each teacher teaches a class during 5 of the 6 class periods and has one class period free. No students have a free class period. How many teachers does the school have?

A. 25
B. 30
C. 36
D. 60
E. 150

PS15402.01
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King School has an enrollment of 900 students. The school day consists [#permalink]
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gmatt1476 wrote:
King School has an enrollment of 900 students. The school day consists of 6 class periods during which each class is taught by one teacher. There are 30 students per class. Each teacher teaches a class during 5 of the 6 class periods and has one class period free. No students have a free class period. How many teachers does the school have?

A. 25
B. 30
C. 36
D. 60
E. 150

PS15402.01

No student has a free period.
Thus, all 900 students are taught each period, implying that each period is composed of the same number of 30-student classes.
Every teacher teaches 5 of the 6 periods.
Thus, every teacher teaches exactly 5 classes.

We can PLUG IN THE ANSWERS, which represent the number of teachers.
When the correct answer is plugged in, the total number of students taught each period = 900.

B: 30
Since each of the 30 teachers teaches 5 classes, the total number of classes = 30*5 = 150.
Since these 150 classes are divided equally among 6 periods, the number of classes per period $$= \frac{150}{6} = 25$$.
Since each of these 25 classes is composed of 30 students, the total number of students taught each period = 25*30 = 750.
Too small.

D: 60
Doubling the number of teachers from 30 to 60 will double the number of students taught each period from 750 to 1500.
Too big.

Since B yields a result that is TOO SMALL and D a result that is TOO BIG, the correct answer must be BETWEEN B AND D.

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Re: King School has an enrollment of 900 students. The school day consists [#permalink]
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gmatt1476 wrote:
King School has an enrollment of 900 students. The school day consists of 6 class periods during which each class is taught by one teacher. There are 30 students per class. Each teacher teaches a class during 5 of the 6 class periods and has one class period free. No students have a free class period. How many teachers does the school have?

A. 25
B. 30
C. 36
D. 60
E. 150

PS15402.01

There are 900 students, and there are 30 students per class.
900/30 = 30
So, at any given time during the school day, there are 30 class periods happening.

Since there are 6 class periods per day, the TOTAL number of classes each day = (6)(30) = 180

Each teacher teaches 5 classes per day
If there are 180 classes per day, then the number of teachers = 180/5 = 36

Cheers,
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Re: King School has an enrollment of 900 students. The school day consists [#permalink]
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gmatt1476 wrote:
King School has an enrollment of 900 students. The school day consists of 6 class periods during which each class is taught by one teacher. There are 30 students per class. Each teacher teaches a class during 5 of the 6 class periods and has one class period free. No students have a free class period. How many teachers does the school have?

A. 25
B. 30
C. 36
D. 60
E. 150

PS15402.01

Since there are 900 students in the school and each student has to attend 6 classes, there are 900 x 6 = 5400 student-class units.

Since each teacher has to teach 5 classes and each class has 30 students, one teacher can manage 5 x 30 = 150 student-class units.

Therefore, we need 5400/150 = 36 teachers.

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King School has an enrollment of 900 students. The school day consists [#permalink]
gmatt1476 wrote:
King School has an enrollment of 900 students. The school day consists of 6 class periods during which each class is taught by one teacher. There are 30 students per class. Each teacher teaches a class during 5 of the 6 class periods and has one class period free. No students have a free class period. How many teachers does the school have?

A. 25
B. 30
C. 36
D. 60
E. 150
PS15402.01

Totol no: of students = 900
No. of students/class = 30
No. of classes = 900/30 = 30
No. of periods/teacher = 5
No. of periods/day = 30*6 = 180

No. of teachers = 180/5 = 36
Option C
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King School has an enrollment of 900 students. The school day consists [#permalink]
MBA HOUSE KEY CONCEPT: rule of 3 directly proportional

900 students

1 day = 6 class periods

1 class period = 1 teacher

30 students = 1 classroom

I00 students / 30 students = 30 classrooms x 6 class periods = 180 class periods / 5 teachers = 36 teachers.

C
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King School has an enrollment of 900 students. The school day consists [#permalink]
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gmatt1476 wrote:
King School has an enrollment of 900 students. The school day consists of 6 class periods during which each class is taught by one teacher. There are 30 students per class. Each teacher teaches a class during 5 of the 6 class periods and has one class period free. No students have a free class period. How many teachers does the school have?

A. 25
B. 30
C. 36
D. 60
E. 150

PS15402.01

Sharing my approach to this PS question

1. We are given that there are a total $$900$$ students and there are $$30$$ students per class. Hence, we have $$\frac{900}{30}$$ $$=$$ $$30$$ classes
2. Each class has $$6$$ periods, hence all $$30$$ classes have $$30 * 6$$ $$=$$ $$180$$ periods
3. Next, we are given that each teacher teaches $$5$$ out of $$6$$ periods, meaning that if there are $$n$$ teachers then a total of $$5n$$ periods are taught. And from step no. 2 we know that the value of $$5n$$ is $$180$$
4. $$5n = 180$$, hence $$n = 36$$

Ans. C
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Re: King School has an enrollment of 900 students. The school day consists [#permalink]
gmatt1476 wrote:
King School has an enrollment of 900 students. The school day consists of 6 class periods during which each class is taught by one teacher. There are 30 students per class. Each teacher teaches a class during 5 of the 6 class periods and has one class period free. No students have a free class period. How many teachers does the school have?

A. 25
B. 30
C. 36
D. 60
E. 150

PS15402.01

The school has 900 students.
30 students in one class therefore school has 30 classes.
Number of periods in school in a day=30*6=180 periods.
Number of periods teachers take in a day=5

Therefore number of teachers=180/5=36 teachers.

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Re: King School has an enrollment of 900 students. The school day consists [#permalink]
There are 30 classes. If all the teachers take their classes 1,2,3,4,5 and keep the last period/class free.. dont we need 30 +30 =60 teachers ?

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Re: King School has an enrollment of 900 students. The school day consists [#permalink]
Hi Sks0106,

Based on your description, I assume that you would have 30 teachers to cover the first 5 periods of the day and then 30 other teachers to cover the 6th period of classes. However, that last group of teachers would ONLY be teaching during the 6th period - and that is not what the question describes (each teacher must cover a class for 5 of the 6 periods).

We're told that King School has an enrollment of 900 students. The school day consists of 6 class periods during which each class is taught by one teacher and there are 30 students per class. However, each teacher teaches a class during 5 of the 6 class periods and has one class period free (but NO students have a free class period). We're asked for the number of teachers that the school has. This question provides us with all of the 'numbers' that we need to answer the question, but you can still perform the necessary calculations in a number of different ways. As such, how you organize your information will impact how quickly you can answer the question.

To start, since each class consists of 30 students, we know that 900/30 = 30 classes run each period.

Since the School runs 6 class periods a day, we will need (6)(30) = 180 teacher-periods to be covered by the teachers.

Each teacher covers 5 teacher-periods a day though (NOT 6), so we need 180/5 =36 teachers to cover all of the classes.

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Re: King School has an enrollment of 900 students. The school day consists [#permalink]
Hi all,

I am having trouble finding similar related problems, so I tried to write one myself . Any insight on the below example would be great (ie. is this question properly testing the same concept and is the answer correct?). Thanks!

A sports camp has 100 campers and there are 20 campers per group at the camp. The camp offers 5 sports and each group must play each sport once per day. If each counselor supervises X number of sports each day, how many counselors does the camp require, in terms of X?

Solution:

1) Calculate number of groups of campers = 100/20=5,

2) Calculate number of sports played total = 5 groups * 5 sports per group = 25 sports total

3) Calculate number of counselors needed to supervise 25 sports = 25 sports / X sports per counselor --> so, total number of counselors required = 25/X

Thanks again

E
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Re: King School has an enrollment of 900 students. The school day consists [#permalink]
900 Total Students. Each student is in a class during each period.

Period 1:

900 students / 30 students per class = 30 classes

Period 2:

900 students / 30 students per class = 30 classes

Etc. for the next 4 periods

Which gives us a Total Number of Classes = (30 classes per period) * (6 periods) =

180 classes————30 classes per period

Finally, we are told that teachers can only teach for 5 periods and need a 6th period off.

Therefore, any 1 teacher can only possibly cover 5 classes.

(180 classes) / (5 classes per 1 teacher) = 36 teachers required

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King School has an enrollment of 900 students. The school day consists [#permalink]
King School has an enrollment of 900 students.

There are 30 students per class and 6 periods per day.

This means in total there 180 class sessions occurring each day.

Teachers only teach 5 periods each: 180/5 = 36 teachers

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Re: King School has an enrollment of 900 students. The school day consists [#permalink]
Number of classrooms = 900/30 = 30
Number of classes taught per day = 30 * 6 = 180
Given each teacher teaches 5 classes per day, therefore, number of teachers = 180 / 5 = 36
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Re: King School has an enrollment of 900 students. The school day consists [#permalink]
gmatt1476 wrote:
King School has an enrollment of 900 students. The school day consists of 6 class periods during which each class is taught by one teacher. There are 30 students per class. Each teacher teaches a class during 5 of the 6 class periods and has one class period free. No students have a free class period. How many teachers does the school have?

A. 25
B. 30
C. 36
D. 60
E. 150

PS15402.01

900 students with 30 students per class means there are $$900/30$$ classes in total = 30 classes in school.

and each class has 6 periods a day, so $$30*6= 180$$periods in 1 day.

so, we need the total $$# teachers * 5$$ ( as each teacher teaches only 5 periods), such that result = $$180$$

when plugging value, always start with the middle, C, in this case,$$36*5= 180$$, directly gives the answer. so good for us.
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Re: King School has an enrollment of 900 students. The school day consists [#permalink]

Each teacher teaches a class during 5 of the 6 class periods and has one class period free.

From the line above, Can I say that

Total periods = 6. Each teacher conducts 5 classes. 1 period maybe break.

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